The disgrace of David Petraeus shouldn’t damage the Central Intelligence Agency. Congress may summon or subpoena the former director and his paramour to testify about their relationship; it may lash them for the sins of pride and lust; it may even try to blame the death of an American ambassador in Libya on a distracted CIA. That would be a waste of time and breath.

But the Petraeus affair may well tarnish the Federal Bureau of Investigation. And maybe it should. There are more than a few bad actors in this tragicomedy. Worst of all, as far as we know now, it was an FBI agent — identified by the New York Times as Frederick W. Humphries II — who took it upon himself to transmit a raw report on the case to a member of Congress. That isn’t whistle-blowing. It has nothing to do with the rule of law or the national security of the U.S. The singular significant fact of the affair thus far is the way in which it came to light. The agent, and the FBI as an institution, should be called to account.

The bureau has the awesome power to destroy anyone in the U.S. by searching their computers, rifling their records, reading their mail and stealing their secrets. It can do that under law, with a judge’s warrant. Or it can ruin people for no real reason, as it did for decades under J. Edgar Hoover.

The CIA as an institution has reason to resent the conduct of the FBI in this case. It would be a disaster if that resentment revives the long-standing rivalry between the agencies. For more than 50 years, they were at each others’ throats, constantly skirmishing and sniping. And the more they made war, the less safe Americans were.

Their failure to cooperate contributed mightily to the success of the Sept. 11 attacks, as the 9/11 commission concluded. The national security chief at the FBI, John O’Neill, and the head of the CIA’s bin Laden desk, Michael Scheuer, refused to share crucial intelligence. They built walls between their agencies, mortared with mutual hatred. After O’Neill was killed inside the World Trade Center during the attack, Scheuer testified in public that his death was “the only good thing” that happened that day.

Hoover started the battle himself. He was a hater, and he truly despised the CIA from the day of its creation after World War II. He saw it as a rival for power; he cursed it as a haven for communist sympathizers; he cultivated secret informers within its walls. “It is a tragedy that the true phoniness of CIA isn’t exposed,” he wrote in royal blue ink on one of his innumerable broadsides against the agency.

Hoover’s political warfare drove his Cold War counterpart, Allen Dulles, the CIA’s chief from 1953 to 1961, to deep despair. “How in the world can I do business with the bureau?” Dulles shouted at his FBI liaison. “I try, and you keep striking back.”

But the balance of power always lay with the bureau, and that power came from presidents. Franklin D. Roosevelt gave Hoover the secret authority to eavesdrop on Americans, to plant hidden microphones in their bedrooms and boardrooms, and to purloin secrets through burglary and break-ins. When the U.S. Supreme Court outlawed telephone wiretaps, Roosevelt told Hoover: To hell with the court. Harry Truman worried aloud that the bureau would become an “American Gestapo.” John F. Kennedy knew Hoover had 20-year-old sex tapes of his tryst with a suspected Nazi agent; he shared his national security adviser’s opinion that Hoover was “a goddamned sewer” collecting and disseminating dirt.

Presidents want the bureau to give them secret intelligence (and sometimes political scuttlebutt). It serves as a sword and a shield. But in the FBI’s hands, the sword can cut both ways.

Unique among federal agencies, the bureau can break presidents. Richard Nixon fell because the FBI fearlessly investigated Watergate (and secretly leaked the facts to reporters). FBI agents made felony cases against Ronald Reagan’s national security team in the Iran-contra imbroglio (Reagan protected himself by appointing the bureau’s director to take over the CIA). The FBI literally drew blood from Bill Clinton; the DNA evidence led to his impeachment for lying about sex.

The bureau’s current director, Robert S. Mueller III, deserves great credit for trying to make peace between the bureau and the agency. That hasn’t been an easy task, but his endurance in office has been a blessing. The CIA, deposed from pre-eminence in the American intelligence establishment, discredited by bogus reporting on phantom weapons of mass destruction in Iraq, dishonored by brutal interrogations of suspected terrorists in secret prisons, rarely keeps its directors for long; five men have held the post in the past eight years. By contrast, Mueller — who took office, God help him, on Sept. 4, 2001 — has served with quiet distinction for more than 11 years in the J. Edgar Hoover Building.

In Hoover’s day, instructors at the FBI Academy taught newly hired agents to revere Hoover by citing the words of Ralph Waldo Emerson: “An institution is the lengthened shadow of one man.” Hoover ruled by fear. He invented the modern surveillance state. And we still live in his shadow.

Mueller cannot sandblast Hoover’s name off the FBI headquarters. He can come out of the building and rule that the FBI agent in this case was out of bounds. Backhanding raw case files to Congress is outside the law. For an agent to decide that he alone knows what is best for the U.S. — a decision that destroyed the director of the CIA — is a dirty business. At the least, a confession of error made by Mueller in public — and by the agent, preferably under oath — might help prevent renewed hostilities between the nation’s two best known intelligence services.

Mueller should make clear to the American people that the FBI will not and cannot conscience a return to an era of backstabbing and blackmail. That kind of blood sport was supposed to have died with Hoover, 40 long years ago.

Tim Weiner, a former reporter for the New York Times, is the author of “Enemies: A History of the FBI” and “Legacy of Ashes: The History of the CIA.” He wrote this column for Bloomberg View. His email address is tiwein@hotmail.com.

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